Are you the employee's supervisor?
It's hard to determine whether you'll "hurt this employee's feelings" or not--the employee may "know" that he has a problem and doesn't care. But if you "hurt his feelings," that's his problem--your job is to concentrate on YOUR problem...which is that his BO is screwing up your firm's operations.
Has he been employed with your firm for a long time?
Did he just recently interview and was hired (did he smell great during the interview?) If so, there should be no "hurting his feelings" he already showed you he knows what to do--you just need to remind him that proper hygiene is expected on the job.
Was he employed for a long time and recently started having this problem? This might be a bit more touchy--maybe his house was foreclosed on and he's living in a car with limited access to shower/laundry facilities. In which case you can offer up some suggestions (is there facilities at/near your workplace where he can get showered each day and launder his clothes?)
Or have you recently been hired and this "problem" has been plunked on your desk. In which case, you'll have to do a bit of investigative work to see if either of the above scenarios are possible.
In the end, if you're the boss, you must handle this quickly and discretely since it is screwing up your firm's productivity and ultimately, profits.
Before the employee leaves for the day, call him into your office and tell him "you're" feeling a bit uncomfortable discussing this delicate situation about his hygiene, but it's important to "both" of you to get it resolved. Ask if there are any problems (medical, etc.) that you may be unaware of for his hygiene issues; listen to his explanation and determine if it is a real problem or just laziness--be prepared to offer up solutions or recommendations. If there are no issues aside from him just not wanting to bathe and wear clean clothes, then you must let him know what you expect and have him report to your office the next day to show you he understands your policy. Praise his efforts and let him know that that is what you expect...then you'll have keep you eye on him from time-to-time to ensure he keeps up the standard you set.
If it turns out that he's just a lazy, dirty, slob...you'll may very well end up firing him.
....being a boss sometimes is a b!tch, ain't it?
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